A simple presentation of the effective topos

Alexis Bernadet 1 Stéphane Graham-Lengrand 1, 2
2 PARSIFAL - Proof search and reasoning with logic specifications
Inria Saclay - Ile de France, LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : We propose for the Effective Topos an alternative construction: a realisability framework composed of two levels of abstraction. This construction simplifies the proof that the Effective Topos is a topos (equipped with natural numbers), which is the main issue that this paper addresses. In this our work can be compared to Frey's monadic tripos-to-topos construction. However, no topos theory or even category theory is here required for the construction of the framework itself, which provides a semantics for higher-order type theories, supporting extensional equalities and the axiom of unique choice.
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  • HAL Id : hal-00844250, version 1
  • ARXIV : 1307.3832

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Alexis Bernadet, Stéphane Graham-Lengrand. A simple presentation of the effective topos. [Research Report] LIX, Ecole polytechnique. 2012. ⟨hal-00844250⟩

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